梯形网格伪谱法地震波场模拟

Seismic wave simulation using a trapezoid grid pseudo-spectral method

波动方程的数值求解是地震勘探高精度成像和反演方法的核心。为保证精度,常规方法往往根据模型最小速度设置固定的空间采样间隔,易在高速区形成"过采样",计算存在一定冗余性。由于重力引起的岩石压实效应,波的传播速度由浅入深整体增大,梯形坐标变换更契合这种速度变化趋势。为此,提出梯形网格伪谱法地震波模拟方法。利用基于梯形坐标变换的梯形网格法对介质进行剖分,在浅层低速区采用细网格、深部高速区采用粗网格,可有效减少网格点数;同时,通过伪谱法求解坐标变换后的变系数声波方程,并引入完全匹配层消除人工边界虚假反射,以兼顾波场模拟的效率与精度。Marmousi模型的测试结果表明,相较于常规固定网格剖分,梯形网格剖分的网格数可减少约69%;相较于常规网格伪谱法和高阶有限差分法,梯形网格伪谱法的计算时间分别减少约58%和60%,同时具有较小的数值频散。可见,所提方法是一种高效、高精度地震波模拟方法。

The numerical solution to wave equation is the computational engine of many high-precision imaging and inversion methods in seismic exploration.In order to ensure the accuracy,regular methods generally set a fixed spatial sampling interval according to the minimum velocity of the model.This always causes over sampling in high velocity layers,and the calculation is redundant to some extent.Under the compaction of rocks cause by gravity,the wave propagation speed usually increases along with depth.The trapezoid coordinate transformation can incorporate the general increasing trend of wave velocity.So,we propose seismic wave simulation using a trapezoid grid pseudo-spectral method.We use the trapezoid grid based on trapezoid coordinate transformation to divide medium.The fine grid is used in the shallow low velocity region and the coarse grid is used in the deep high velocity region,which can effectively reduce the number of sampling points.Meanwhile,considering the accuracy of wave field simulation,we use pseudo-spectral method to solve the acoustic wave equation with variable coefficients after coordinate transformation and use the perfectly matched layer to eliminate the fictitious return wave caused by artificial boundary.The test on Marmousi model shows that comparing with the general method,the number of grids generated by trapezoidal grid can reduce 69%,and comparing with the regular grid pseudo-spectral method and the high order finite difference method,the calculation time of trapezoidal grid pseudo-spectral method can respectively reduce 58%and 60%.Therefore,this method is an efficient and high-precision seismic wave simulation method.